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ABCDE is a regular pentagon. A point P is taken inside this pentagon such that ∆CDP is an equilateral triangle. What is ∠BPE ?
- a)150°
- b)160°
- c)168°
- d)176°
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
ABCDE is a regular pentagon. A point P is taken inside this pentagon s...
∠BCD = 108°
So, ∠BCP = 48°
ΔBPC is isosceles.
So, ∠BCP = 66°
Hence, θ = 360° - 60° - 2 x 66°
► θ = 360° - 60° - 132°
► θ = 360° - 192°
► θ = 168°
Most Upvoted Answer
ABCDE is a regular pentagon. A point P is taken inside this pentagon s...
To find the measure of angle BCD, we need to consider the properties of a regular pentagon.
In a regular pentagon, each interior angle measures 108 degrees. Therefore, angle ABC measures 108 degrees.
Since angle CDP is an equilateral triangle, each angle measures 60 degrees. Therefore, angle DCP measures 60 degrees.
The sum of the angles in triangle BCD is 180 degrees. Therefore, angle BCD can be found by subtracting the measures of angles DCP and BCD from 180 degrees:
BCD = 180 degrees - 108 degrees - 60 degrees = 12 degrees.
So, the measure of angle BCD is 12 degrees.
In a regular pentagon, each interior angle measures 108 degrees. Therefore, angle ABC measures 108 degrees.
Since angle CDP is an equilateral triangle, each angle measures 60 degrees. Therefore, angle DCP measures 60 degrees.
The sum of the angles in triangle BCD is 180 degrees. Therefore, angle BCD can be found by subtracting the measures of angles DCP and BCD from 180 degrees:
BCD = 180 degrees - 108 degrees - 60 degrees = 12 degrees.
So, the measure of angle BCD is 12 degrees.
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ABCDE is a regular pentagon. A point P is taken inside this pentagon such that CDP is an equilateraltriangle. What is ∠BPE ?a)150°b)160°c)168°d)176°Correct answer is option 'C'. Can you explain this answer?
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